The present invention relates to a method and apparatus for, via skiving, finishing the flanks of the teeth of a cylinder wheel that is provided with internal or external spur or helical gearing, whereby the right and left flanks of the teeth are generated in separate operations and, to produce helix modifications, such as tooth crowning, and/or end relief, the pertaining apparatus, depending on the movement of the axial carriage, alters the center distance between tool and workpiece, and/or alters the additional rotation of the workpiece relative to the tool.
Skiving is a continuously carried-out process for producing cylindrical gears by cutting. The tool is similar to a gear-type shaping cutter; however, its axis of rotation is crossed with the axis of the workpiece. During machining, the tool and the workpiece carry out a basic rotation In so doing, the speeds of rotation are in inverse ratio to the numbers of teeth of the two elements. Superimposed over the basic rotation, the tool carries out a helical movement relative to the workpiece. This helical movement comprises a displacement of the tool in the direction of the workpiece axis, and an additional rotation of the workpiece that is proportional to this displacement. The additional rotation is calculated in such a way that where a workpiece is being machined without helix modifications, the additional rotation is 2.pi. if the axial displacement is equal to the lead of the gear toothing to be produced. Thus, the following equations apply ##EQU1## where .DELTA.Z=axial carriage displacement
.DELTA..rho.=angle of additional rotation PA1 H=lead of the workpiece PA1 b=face width PA1 z=coordinate in direction of the workpiece axis relative to the center of the tooth width PA1 F.sub..beta. =helix deviation (or helix modification) PA1 I=reference face of the gear PA1 II=non-reference face of the gear
In practice it is frequently desirable rather than forming the flanks of cylindrical teeth exactly as involute helicoids, to modify profile and helix. For example, the gearing should be cut with tooth crowning and profile barrelling. The description of these modifications is conventionally done with the aid of profile- and helix diagrams.
Flank modifications can be produced via skiving. As a first approximation one can say profile modifications are produced via a modification of the tool profile, and helix modifications are produced via a modification of the machine movements.
However, upon closer analysis, it can be seen that the modification of the machine movements also influences the workpiece profile. This influence leads, for example, to the formation of distorted flanks during the skiving of crowned teeth. This distortion means that in different transverse sections, profiles with differing profile slope deviations exist, and on different cylinders helix deviations with different helix slope components exist.
The occurrence of this distortion is explained with the aid of FIGS. 1a and 1b.
FIGS. 1a and 1b show the right flank of a left-hand helical cylinder gear.
The terms are as follows:
The term "reference face" is needed to designate the respective flank as the right or left flank. The helix deviation is measured on the measurement cylinder, in FIG. 1a on the line F.sub.1 F.sub.1 ', and the profile deviation is measured in the center of the tooth width in the transverse section, i.e. the line P.sub.1 P.sub.1 '. Deviations of the flank from the pertaining unmodified involute helicoid are to be imagined perpendicular to the plane of the drawing.
To facilitate understanding, it should first be assumed that all traces of the tool on a flank have the same course, and all points of a trace are at the same distance from the unmodified involute helicoid, in other words are disposed by the same amount above or below the plane of the drawing. Naturally, when the surface geometry is calculated with the aid of a computer, the simplifications formulated above are not needed.
A course of the helix "deviation" is prescribed in conformity with the representation of FIG. 1b. On the measurement cylinder (FIG. 1a) the high point of the flank is in the center of the face width; in the root area of the toothing, the high point is at S.sub.1, and in the tip area at S.sub.1 '. On each cylinder, between the root-form and tip form cylinder practically the same curve of the helix deviation exists. Merely the high point is shifted in the direction Z in conformity with the z-component of the trace S.sub.1 S.sub.1 '. Since the length of the F.sub..beta. diagram is always equal to the face width, on various measurement cylinders always a somewhat different region of the prescribed curve will be measured. Therefore, to describe the course of F.sub..beta. in the root area of the toothing the curve is to be extended on face II, and to describe the course in the tip area of the toothing the curve is to be extended on the face I relative to the course on the prescribed measurement cylinder.
The profile deviation in a particular transverse section is the distance of the respectively considered point from the unmodified involute helicoid. In conformity with the aforementioned statements, one obtains, for example, the profile deviation in the middle of the face width at the locations P.sub.1 (root form circle) or P.sub.1 ' (tip form circle) as the distance of the traces that extend through these points from the unmodified involute helicoid. P.sub.1 consequently has the same distance as point H.sub.6 from the unmodified involute helicoid, namely the distance H.sub.6 'H.sub.6 "; similarly, P.sub.1 ' has the distance H.sub.2 'H.sub.2 ". If this procedure is carried out for further points between P.sub.1 and P.sub.1 ', one sees that the course of the profile deviation F.sub..alpha. in the middle of the face width is the same as the course of the helix deviation F.sub..beta. between H.sub.6 ' over H.sub.1 ' to H.sub.2 '.
If the previously formulated considerations relative to the helix deviations on the root-form or the tip form cylinder and relative to the profile deviations in planes I and II are applied, the following results will be obtained:
______________________________________ Measuring Measurement Measured plane of between the Course of parameter cyliner points the deviation ______________________________________ F.sub..alpha. I P.sub.2 -P.sub.2 ' H.sub.3 '-H.sub.4 '-H.sub.5 ' Middle of P.sub.1 -P.sub.1 ' H.sub.6 '-H.sub.1 '-H.sub.2 ' the face width II P.sub.3 -P.sub.3 ' H.sub.9 '-H.sub.8 '-H.sub.7 ' F.sub..beta. Root form cylinder F.sub.3 -F.sub.3 ' H.sub.3 '-H.sub.9 ' Prescribed F.sub.1 -F.sub.1 ' H.sub.4 '-h.sub.8 ' measuring cylinder Tip form cylinder F.sub.2 -F.sub.2 ' H.sub.5 '-H.sub.7 ' ______________________________________
If the results are plotted graphically, the illustrations of FIGS. 2a-2f are obtained. In these illustrations, the deviation existing at the respective point is designated by the symbol "q", i.e. EQU q.sub.1 =H.sub.1 ' H.sub.1 "=0 EQU q.sub.2 =H.sub.2 ' H.sub.2 " EQU q.sub.3 =H.sub.3 ' H.sub.3 "
Furthermore, F.sub..beta.Ff designates the helix deviations on the root form cylinder, and F.sub..beta.Fa designates the helix deviations on the tip form cylinder.
With the exception of the points on the trace S.sub.1 S.sub.1 ', all of the points of the modified flank are recessed from an unmodified involute helicoid; the values q.sub.2 . . . q.sub.9 therefore have a negative sign.
If the helix slope deviation on the root form cylinder is designated with the symbol f.sub.H.beta.f, and the deviation on the tip form cylinder is designated with the symbol f.sub.H.beta.a, the following equations are obtained EQU f.sub.H.beta.f q.sub.3 -q.sub.9 EQU f.sub.H.beta.a =q.sub.5 -q.sub.7
The distortion of the helices is EQU .DELTA.f.sub.H.beta. =f.sub.H.beta.a -f.sub.H.beta.f.
From the profile slope deviations EQU f.sub.H.alpha.I =q.sub.5 -q.sub.3
in plane I, and EQU f.sub.H.alpha.II =q.sub.7 -q.sub.9
in plane II, the distortion of the profiles is EQU .DELTA.f.sub.H.alpha. =f.sub.H.alpha.I -f.sub.H.alpha.II
It should be noted that in this example .DELTA.f.sub.H.beta. and .DELTA.f.sub.H.alpha. have a negative sign. This can be easily seen from the values illustrated in FIGS. 1a, 1b and 2a-2f.
The previously mentioned statements relate to the right flanks of a left-hand helical toothing. The observations can be easily transferred to the remaining situations, in other words to the left flanks of the left-hand helical toothing and to the two flanks of a right-hand helical toothing or a spur toothing. For this purpose, it is merely necessary to have the course of the tool trace on the respective workpiece flank.
The trace can be calculated together with the tool design or with the simulation of the finishing process. Also in the remaining situations, i.e. in particular with a spur toothing, the trace extends obliquely over the workpiece flank. FIGS. 3a-3h shows in principle the courses of the traces for the aforementioned situations.
With skiving, a spur toothing can be machined only with a helically toothed tool. The sign of the "inclination" of the traces depends in this connection upon the sign of the helix of the tool. Consequently, with spur toothed workpieces the two outlined curves for the traces result.
Whereas with the right flank of the left-hand helical toothing the points of the trace in the tip area of the workpiece toothing are closer to the plane II than in the root area, these points of the left flank of the left-hand helical toothing are closer to the plane I. When using the previously described calculation process, one discovers that the distortion of the helices and the distortion of the profiles of the left flanks of the left-hand helical toothing have a positive sign. It has already been mentioned that corresponding values of the right flanks have a negative sign. It is also true in the remaining situations that the profiles and of the helices has an opposite sign on the right flank compared with the respective sign of the distortion of these values on the left flank.
The distortion of the flanks of cylinder wheels that are finished via skiving, as characterized by the distortions of profile and helix, is frequently undesired. It is therefore an object of the present invention to further develop the method and apparatus of the aforementioned type in such a way that the distortion of the flanks is brought to a desired value, and possibly is avoided or at least is reduced to a negligibly small value.